Question 1: [40 marks] xy A surface is defined by the following equation: z(x, y) = a) Find the equation of the tangent plane to the surface at the point P(3, 5). Present your answers in the exact form (don't use a calculator to convert your result to the floating- point format). [25 marks] b) Find the gradient of function z (x, y) at the same point P. [5 marks] c) Find the angle between the gradient and the x-axis. Present your answer in degrees up to one decimal place. [10 marks] Rubric: 3 marks if zo was correctly calculated; 5 marks for correctly calculated a partial derivative with respect to x; 3 marks if number p was correctly calculated; 5 marks for correctly calculated a partial derivative with respect to y; 3 marks if number q was correctly calculated; 5 marks if equation of the tangent plane was correctly presented; 4 marks if equation of the tangent plane was properly simplified and presented in the exact form; 5 marks if the gradient was correctly presented at the point P; 4 marks if the angle a was found correctly; 3 marks if the angle a was correctly presented in degrees up to one decimal place